The Independence Axiom versus the Reduction Axiom: Must We Have Both?

Since the early 18th Century, expected utility theory became the leading theory in explaining behavior of decision makers under uncertainty. For most of this time it was used as a purely descriptive theory. For example, Ramsey (1931) explicitly assumed that people evaluate a risky prospect by its expected utility. He expressed this idea in the following words: I suggest that we introduce as a law of psychology that his Ithe decision maker's] behavior is governed by what is called the mathematical expectation: that is to say that, if p is a proposition about which he is doubtful. any goods or bads for whose realization p is in his view a necessary and sufficient condition enter into his calculations multiplied by the same fraction, which is called the 'degree of his belief in p'.